Compact differences of composition operators on weighted Dirichlet spaces

作者：Allen Robert F^*; Heller Katherine C; Pons Matthew A

来源：Central European Journal of Mathematics, 2014, 12(7): 1040-1051.

DOI：10.2478/s11533-013-0397-3

• Composition operator
• Compact difference
• Weighted Dirichlet space
• Complex interpolation

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces D-alpha. Specifically we study differences of composition operators on the Dirichlet space D and S-2, the space of analytic functions whose first derivative is in H-2, and then use Caldern's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

• 出版日期2014-7